Diffraction is a large subject with some fairly difficult mathematics - the
intention here is just to cover the basics. Skip the equations if you like.

Consider figure 1 - a plane wave comes across an obstruction, the energy above
the obstruction passes and the rest is blocked. This does not happen in reality
and the reason is diffraction. Figure 2 shows a more likely result.

Figure 1 - Not reality

In reality, there is diffraction around the barrier as shown with
some exaggeration in figure 2.

Figure 2 - More like what happens

The Huygens principle of wavelets can be used to explain this - “Each
point on a wavefront acts as a source of secondary wavelets. The combination
of these secondary wavelets produces the new wavefront in the direction of propagation”.We
can express this as an integral:

Where v is the height of the obstruction. Fortunately, this is solvable with
a few substitutions:

This is tricky to solve by hand but there is an approximation
for v >1

When is Diffraction Significant - Fresnel Zones

An obstruction is generally considered to be significant when it impinges into
the first Fresnel zone.

The first Fresnel ellipsoid is bounded by the ellipses where the path length
from transmitter to receiver is exactly a half wavelength longer, the second
where the path length difference is one and a half wavelengths etc etc. I.e.
the area inside the contour where Dl
< l/2 is the first Fresnel zone. Dl
< 3l/2 is the second etc.

Figure 3 - Fresnel Ellipsoids

Putting it into Practice

The theory above is a simplification, but it is still not practical to apply
easily. The result for the signal amplitude
after an ideal knife edge is shown in figure 4. This can be used to calculate
the diffraction loss as a function of the Fresnel parameter v as defined above.

Figure 4- Knife Edge Diffraction

It is notable that as the knife edge comes into the first Fresnel
zone the amplitude rises and then falls fairly linearly, this function can be
approximated for v >-0.7 as:

Approximation for Fresnel integral for knife edge

Diffraction around real objects

Most real-world obstructions are large in comparison to the wavelength - i.e.
not knife edges. It is possible to solve the equations for idealised cases.
Solutions for many objects and including reflection effects, loss from trees
etc. rapidly become impractical. Therefore path loss prediction models are used.

There are several models in general these involve adding additional
loss to the knife edge loss. Where there are multiple knife edges further models
are available, the one currently used by the ITU-R for terrestrial links is
a modified version of the Deygout model. More information is available in Recommendation
ITU-R P.526 - Propagation by Diffraction. If there is demand, I will include
some of the models here. A diffraction model is included in the pathloss
software

Frequency

Higher frequencies have shorter wavelengths and therefore smaller
Fresnel zones. As a result, as frequency increases for a given partially obstructed
path, less and less of the first Fresnel zone is obstructed. However, as the
Fresnel zone is smaller, the increase in diffraction loss with increasing obstruction
(e.g. as the height of the receiver is lowered) happens much more quickly.